A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

Mishra, Shashi Kant; Chakraborty, Suvra Kanti; Samei, Mohammad Esmael; Ram, Bhagwat

doi:10.1186/s13660-021-02554-6

Journal of Inequalities and Applications

Table 1 q-Gradient of Example 5.1

From: A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

k	\(q^{k}\)	\(x=(2.88, 1.82)^{T}\)
k	\(q^{k}\)	f(x)	\(f(q^{k}x)\)	\(g_{q^{k}}(1)\)	\(g_{q^{k}}(2)\)
1	\((0.32, 0.32)^{T}\)	0.430480518	1.076549247	−0.74986965	−0.52203356
2	\((0.92, 0.92)^{T}\)	0.430480518	0.542260247	−0.39724386	−0.76771792
3	\((0.905955556, 0.905955556)^{T}\)	0.430480518	0.565980670	−0.39444591	−0.79165371
4	\((0.953527001, 0.953527001)^{T}\)	0.430480518	0.490652335	−0.40526797	−0.71141177
5	\((0.966933215, 0.966933215)^{T}\)	0.430480518	0.471966971	−0.40833281	−0.68935502
6	\((0.976520984, 0.976520984)^{T}\)	0.430480518	0.459272296	−0.41026389	−0.67377859
7	\((0.982303255, 0.982303255)^{T}\)	0.430480518	0.451881863	−0.41128298	−0.66447140
8	\((0.986210799, 0.986210799)^{T}\)	0.430480518	0.446999451	−0.41189872	−0.65822064
9	\((0.988952271, 0.988952271)^{T}\)	0.430480518	0.443627482	−0.41229233	−0.65385448
10	\((0.990951471, 0.990951471)^{T}\)	0.430480518	0.441196138	−0.41255827	−0.65068070
11	\(( 0.990951471, 0.992453623)^{T}\)	0.430480518	0.439384557	−0.41274593	−0.64830175
12	\((0.993610749, 0.993610749)^{T}\)	0.430480518	0.437997983	−0.41288317	−0.64647262
13	\((0.994520907, 0.994520907)^{T}\)	0.430480518	0.436912784	−0.41298657	−0.64503597
14	\((0.995249658, 0.995249658)^{T}\)	0.430480518	0.436047321	−0.41306642	−0.64388700
15	\((0.995842177, 0.995842177)^{T}\)	0.430480518	0.435345901	−0.41312939	−0.64295371
16	\((0.996330408, 0.996330408)^{T}\)	0.430480518	0.434769453	−0.41317996	−0.64218527
17	\((0.996737456, 0.996737456)^{T}\)	0.430480518	0.434289902	−0.41322119	−0.64154502
18	\((0.997080367, 0.997080367)^{T}\)	0.430480518	0.433886651	−0.41325527	−0.64100595
19	\((0.997371937, 0.997371937)^{T}\)	0.430480518	0.433544306	−0.41328378	−0.64054780
20	\((0.997621924, 0.997621924)^{T}\)	0.430480518	0.433251172	−0.41330787	−0.64015514
21	\((0.997837873, 0.997837873)^{T}\)	0.430480518	0.432998239	−0.41332843	−0.63981606
22	\((0.998025695 ,0.998025695)^{T}\)	0.430480518	0.432778468	−0.41334611	−0.63952123
23	\(( 0.998190068, 0.998190068)^{T}\)	0.430480518	0.432586299	−0.41336143	−0.63926328
24	\((0.998334740, 0.998334740)^{T}\)	0.430480518	0.432417292	−0.41337480	−0.63903629
25	\((0.998462736 , 0.998462736)^{T}\)	0.430480518	0.432267864	−0.41338653	−0.63883551
26	\((0.998576525 , 0.998576525)^{T}\)	0.430480518	0.432135102	−0.41339690	−0.63865705
27	\(( 0.998678133,0.998678133 )^{T}\)	0.430480518	0.432016614	−0.41340609	−0.63849771
28	\((0.998769240, 0.998769240)^{T}\)	0.430480518	0.431910422	−0.41341429	−0.63835486
29	\((0.998851242, 0.998851242)^{T}\)	0.430480518	0.431814882	−0.41342163	−0.63822631
30	\((0.998925315, 0.998925315)^{T}\)	0.430480518	0.431728614	−0.41342823	−0.63811020
31	\((0.998992449, 0.998992449)^{T}\)	0.430480518	0.431650455	−0.41343419	−0.63800497
32	\((0.999053483, 0.999053483)^{T}\)	0.430480518	0.431579419	−0.41343959	−0.63790932
33	\((0.999109135, 0.999109135)^{T}\)	0.430480518	0.431514666	−0.41344449	−0.63782211
34	\((0.999160020, 0.999160020)^{T}\)	0.430480518	0.431455475	−0.41344896	−0.63774237
35	\((0.999206667, 0.999206667)^{T}\)	0.430480518	0.431401227	−0.41345305	−0.63766929
36	\((0.999249534, 0.999249534)^{T}\)	0.430480518	0.431351386	−0.41345679	−0.63760212
37	\((0.999289018, 0.999289018)^{T}\)	0.430480518	0.431305487	−0.41346023	−0.63754027
38	\((0.999325466, 0.999325466)^{T}\)	0.430480518	0.431263125	−0.41346340	−0.63748317
39	\((0.999359181, 0.999359181)^{T}\)	0.430480518	0.431223946	−0.41346633	−0.63743035
40	\((0.999390431, 0.999390431)^{T}\)	0.430480518	0.431187638	−0.41346903	−0.63738140
41	\((0.999419450, 0.999419450)^{T}\)	0.430480518	0.431153928	−0.41347154	−0.63733595
42	\((0.999446445, 0.999446445)^{T}\)	0.430480518	0.431122572	−0.41347387	−0.63729367
43	\((0.999471599 ,0.999471599)^{T}\)	0.430480518	0.431093358	−0.41347603	−0.63725427
44	\((0.999495078, 0.999495078)^{T}\)	0.430480518	0.431066094	−0.41347805	−0.63721750
45	\((0.999517026, 0.999517026)^{T}\)	0.430480518	0.431040610	−0.41347994	−0.63718313
46	\((0.999537573, 0.999537573)^{T}\)	0.430480518	0.431016755	−0.41348170	−0.63715095
47	\(( 0.999556836, 0.999556836)^{T}\)	0.430480518	0.430994392	−0.41348335	−0.63712078
48	\(( 0.999574921, 0.999574921)^{T}\)	0.430480518	0.430973400	−0.41348490	−0.63709246
49	\((0.999591921 , 0.999591921)^{T}\)	0.430480518	0.430953669	−0.41348635	−0.63706584
50	\((0.999607921, 0.999607921)^{T}\)	0.430480518	0.430935100	−0.41348771	−0.63704079

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